12/15/202012/15/2020 - Daily Challenge Solution


Equations\underline{\text{Equations}}

a+e=4b+i=5f+j=6g+k=7c+l=8d+h=9a+b+c+d=12e+f+g+h=13i+j+k+l=14\begin{aligned} a + e &= 4 \\ b + i &= 5 \\ f + j &= 6 \\ g + k &= 7 \\ c + l &= 8 \\ d + h &= 9 \\ a + b + c + d &= 12 \\ e + f + g + h &= 13 \\ i + j + k + l &= 14 \end{aligned}


Brute-Force Case Work\underline{\text{Brute-Force Case Work}}

aa can be either one of 1,21, 2 and 33.

dd can be either one of 3,4,53, 4, 5 and 66.

Thus, their possible sums are 4,5,6,7,84, 5, 6, 7, 8 and 99.

bb can be either one of 1,2,31, 2, 3 and 44.

cc can be either one of 2,3,52, 3, 5 and 66.

Thus, their possible sums are 3,4,5,6,7,8,93, 4, 5, 6, 7, 8, 9 and 1010.

(Let | be the same as 'or'.)

So, a+b+c+da + b + c + d is the same as [456789]+[345678910][4 | 5 | 6 | 7 | 8 | 9] + [3 | 4 | 5 | 6 | 7 | 8 | 9 | 10]

The only pairs here that make 1212 are [3+9],[4+8],[5+7] and [6+6][3 + 9], [4 + 8], [5 + 7] \text{ and } [6 + 6]

Meh, this is getting nowhere...

Note by A Former Brilliant Member
7 months, 1 week ago

No vote yet
1 vote

  Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

  • Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
  • Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
  • Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
  • Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold

- bulleted
- list

  • bulleted
  • list

1. numbered
2. list

  1. numbered
  2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1

paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
    # 4 spaces, and now they show
    # up as a code block.

    print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.
2 \times 3 2×3 2 \times 3
2^{34} 234 2^{34}
a_{i-1} ai1 a_{i-1}
\frac{2}{3} 23 \frac{2}{3}
\sqrt{2} 2 \sqrt{2}
\sum_{i=1}^3 i=13 \sum_{i=1}^3
\sin \theta sinθ \sin \theta
\boxed{123} 123 \boxed{123}

Comments

Sort by:

Top Newest

INCOMPLETE (and really frustrating...)

A Former Brilliant Member - 7 months, 1 week ago

Log in to reply

Haha bro, I hate problems like those. No point in solving them lol

Krishna Karthik - 7 months ago

Log in to reply

Yes...I abandoned this when I started getting hopeless lol

Log in to reply

It turns out this problem is impossible. If the numbers from 1-10 are only allowed to be used ONCE, then we cannot solve column 1 or 2.

Comment if you want coding proof

Anonymous1 Assassin - 6 months, 2 weeks ago

Log in to reply

×

Problem Loading...

Note Loading...

Set Loading...